Stability And Synchronization Analysis Of Fractional-order Neural Networks

The dynamics of fractional order neural networks has attracted much attention in various research fields in recent years,and lots of relevant literatures on the stability analysis and the synchronization control of the systems have emerged.Even so,there are still many problems to be studied and solved,such as the conservatism and limitation of the construction of energy function when using Lyapunov to analysis the stability of the fractional system,the time delay problem in fractional order neural network system and the construction of controller when realizing the synchronization of fractional order neural network system.Under Riemann-Liouville derivative,this paper mainly studies the stability and system synchronization problem of fractional neural network system.The detailed is depicted as follows:1)A kind of asymptotic stability problems for fractional order neural networks is studied.Firstly,the equilibrium point of the system is proved.According to the topology degree theory and compression mapping theorem,the point is uniqueness.Secondly,using the Lyapunov direct method to analyze the stability of the system.Flexibility to construct suitable functions,then combining with linear matrix inequality(LMI)conditions,and the asymptotic stability criterion is obtained.It avoids the problem that fractional calculus is difficult to derive through Leibniz’s rule.Finally,the rationality of the numerical examples and the conclusions are verified by numerical simulation experiments.2)A kind of asymptotic stability problems for fractional-order neural networks with time delay is studied.Firstly,the equilibrium point of the system is studied.According to the fixed-point theorem and the compression map theorem,the point is uniqueness.Then the prerequisites for analyzing the stability of the system are obtained.Secondly,using the generalized Lyapunov direct method,under the condition that the equilibrium point of the fractional-order system with time delay,a suitable Lyapunov functional is constructed,so the asymptotic stability criterion for time-delay neural network system is obtained.It is a generalization of the integer-order stability analysis method,which expands the selection range of Lyapunov functions.Finally,verify the rationality of the conclusions through numerical simulation experiments.3)According to the stability conclusion given in this paper,an effective control law is designed to realize different types of synchronization between fractional-order chaotic neural networks.For the drive-response model of fractional order chaotic neural network without time delay,the synchronization problem between the two systems of driving and responding is transformed into the stability of the error system.On the basis of the stability conclusions obtained before,a suitable linear feedback controller is designed to achieve complete synchronization,reverse synchronization and projective synchronization between the driving and responding fractional order systems.Through modeling and simulation of numerical examples,the rationality of the methods and control laws used is verified.In addition,for the fractional-order neural network system with time delay,the same method is used.On the basis of the stability conclusion,the linear feedback control law is designed.Finally,through modeling and simulation of numerical examples,the rationality of the methods and control law used is verified.